What is the oblique asymptote for:
f(x) = (x^2 - x - 6)/ (x - 2)
after using long division, you get:
f(x) = x + 1 + 4/(x - 2)
as x approaches infinity, f(x) approaches (x + 1)
oblique asymptote: y = x + 1
You get the oblique asymptote by dividing the leading terms in the numerator and the denominator.
x^2/x = x. That's the equation for the oblique asymptote.
Divide and the quotient is your oblique asymptote
you get the asymptote by dividing the leading coefficient of the numerator by the leading coefficient of the denominator.
in this case it would be x^2 / x = x
therefore, the asymptote is y=x
Comments
f(x) = (x^2 - x - 6)/ (x - 2)
after using long division, you get:
f(x) = x + 1 + 4/(x - 2)
as x approaches infinity, f(x) approaches (x + 1)
oblique asymptote: y = x + 1
You get the oblique asymptote by dividing the leading terms in the numerator and the denominator.
x^2/x = x. That's the equation for the oblique asymptote.
Divide and the quotient is your oblique asymptote
you get the asymptote by dividing the leading coefficient of the numerator by the leading coefficient of the denominator.
in this case it would be x^2 / x = x
therefore, the asymptote is y=x